Best Proximity Point Theorems for p-Proximal α-η-β-Quasi Contractions in Metric Spaces with w0-Distance
Best Proximity Point Theorems for p-Proximal α-η-β-Quasi Contractions in Metric Spaces with w0-Distance作者机构：Department of Mathematics Nanchang University Department of Mathematics Swansea University
出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))
年 卷 期：2022年第42卷第1期
页 面：95-110页
核心收录：
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金：Supported by the National Natural Science Foundation of China (Grant Nos. 12161056 11701259 11771198) the Natural Science Foundation of Jiangxi Province (Grant No. 20202BAB201001)
主 题：best proximity point $p$-proximal $\alpha - \eta - \beta $ quasi contraction ${\omega _0}$-distance $\alpha $-proximal admissible mapping with respect to $\eta $ $\left( {\alpha,d} \right)$ regular mapping with respect to η
摘 要：In this paper, we propose a new class of non-self mappings called p-proximal α-η-β-quasi contraction, and introduce the concepts of α-proximal admissible mapping with respect to η and(α, d) regular mapping with respect to η. Based on these new notions, we study the existence and uniqueness of best proximity point for this kind of new contractions in metric spaces with w-distance and obtain a new theorem, which generalize and complement the results in [Ayari, M. I. et al. Fixed Point Theory Appl., 2017, 2017: 16] and [Ayari, M. I. et al. Fixed Point Theory Appl., 2019, 2019: 7]. We give an example to show the validity of our main ***, we obtain several consequences concerning about best proximity point and common fixed point results for two mappings, and we present an application of a corollary to discuss the solutions to a class of systems of Volterra type integral equations.
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